Problem: Aril and Dita are wealthy Norwegian business owners who make monthly donations to international disaster relief. Aril donated $150$ Norwegian kroners $(\text{kr})$ the first month, and the cumulative number of Norwegian kroners she has donated increases by a factor of $2.5$ each month. Dita donated $300\,\text{kr}$ the first month, and the cumulative number of Norwegian kroners she has donated increases by $400\,\text{kr}$ each month. They started making donations at the same time, and they both make their monthly donations at the beginning of each month. What is the first month in which Aril's cumulative donation exceeds Dita's cumulative donation?
Explanation: Notice that Aril's cumulative total grows exponentially while Dita's cumulative total grows linearly. This means Aril's cumulative total is bound to exceed Dita's cumulative total at some point. Let's start calculating the cumulative donation from each business owner to see when that happens. Month Aril Dita (Multiply by $2.5$ each month.) (Add $400$ each month.) $1$ $150$ $300$ $2$ $375$ $700$ $3$ $937.5$ $1100$ $4$ $2343.75$ $1500$ In conclusion, Aril's cumulative donation will first exceed Dita's cumulative donation in month number $4$.